SEISMIC FRAGILITY CURVES FOR A TYPICAL HIGHWAY BRIDGE IN CHARLESTON, SC CONSIDERING SOIL- STRUCTURE INTERACTION AND LIQUEFACTION EFFECTS

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1 Clemson University TigerPrints All Theses Theses SEISMIC FRAGILITY CURVES FOR A TYPICAL HIGHWAY BRIDGE IN CHARLESTON, SC CONSIDERING SOIL- STRUCTURE INTERACTION AND LIQUEFACTION EFFECTS Matthew Bowers Clemson University, mebower@clemson.edu Follow this and additional works at: Part of the Civil Engineering Commons Recommended Citation Bowers, Matthew, "SEISMIC FRAGILITY CURVES FOR A TYPICAL HIGHWAY BRIDGE IN CHARLESTON, SC CONSIDERING SOIL-STRUCTURE INTERACTION AND LIQUEFACTION EFFECTS" (27). All Theses This Thesis is brought to you for free and open access by the Theses at TigerPrints. It has been accepted for inclusion in All Theses by an authorized administrator of TigerPrints. For more information, please contact kokeefe@clemson.edu.

2 SEISMIC FRAGILITY CURVES FOR A TYPICAL HIGHWAY BRIDGE IN CHARLESTON, SC CONSIDERING SOIL-STRUCTURE INTERACTION AND LIQUEFACTION EFFECTS A Thesis Presented to the Graduate School of Clemson University In Partial Fulfillment of the Requirements for the Degree Master of Science Civil Engineering by Matthew E. Bowers December 27 Accepted by: Dr. Bryant Nielson, Committee Chair Dr. Scott Schiff Dr. Charng-Hsein Juang

3 ABSTRACT Evidence from historical earthquakes suggests that the vulnerability of highway bridges is significantly affected by large permanent ground deformations caused by liquefaction as well as soil-structure interaction (SSI). The vulnerability of a typical multi-span simply-supported (MSSS) concrete girder bridge found in Charleston, South Carolina, is evaluated with consideration for liquefaction and SSI effects. In general, existing bridges in this region were not originally designed with consideration for seismic events or liquefaction of underlying soils. Fragility curves that represent the probability of exceeding predefined performance levels of damage given an earthquake of a particular intensity are used to evaluate the effects of liquefaction and SSI on the performance of the bridge components and the entire bridge system. Because of the lack of earthquake damage data in this region, obtaining analytical bridge models capable of accounting for realistic nonlinear soil and structure behavior is a requirement for creating accurate representations of bridge fragility. To better understand the effects of liquefaction and its possible consequences to the reliability framework, a detailed 2D finite element model representing the MSSS concrete bridge and a typical Charleston soil profile is subjected to a simulation of nonlinear time history ground motions to generate probabilistic seismic demand models (PSDMs). The combined soil-structure model captures constitutive soil behavior, SSI, loss of foundation stiffness due to liquefaction, and structural nonlinearities. Liquefiable dynamic nonlinear springs dependent on the excess pore water pressure of adjacent soil elements are utilized to model the lateral SSI interaction in conjunction with free-field soil columns. Soil columns ii

4 are used to perform a nonlinear seismic response analysis to better understand soil model behavior and the amplification of bedrock ground motions. Simplifying assumptions limited the study of liquefaction to include only the loss of foundation stiffness as a result of increased excess pore pressure buildup. Component fragility curves were created and combined using a joint probabilistic seismic demand model (JPSDM) to form system fragility curves for the MSSS concrete girder bridge. As a result of the limited liquefaction effects included in this study, a few of the stronger ground motions induced noticeable large variations in seismic demand to the displacement dependent bridge components; however, the sensitivity of the model to frequency content and soil profile compositions limited the appearance of liquefaction effects for this particular study. These results suggest that the consideration of the permanent ground deformations associated with liquefaction should be considered as well as the ground shaking hazard, but that additional liquefaction effects including vertical settlement and lateral spreading of the soil need to be considered in the analytical model for the creation of fragility curves considering liquefaction. The use of the dynamic p-y method with free-field soil columns successfully modeled SSI effects and offers the potential to represent liquefaction effectively in the fragility framework. This is particularly true if lateral spreading and vertical settlement caused by liquefaction can be effectively captured by a soil model with fewer simplifying constraints. iii

5 ACKNOWLEDGEMENTS I would like to thank my advisor, Dr. Bryant Nielson, for promoting an environment that emphasized learning as well as integrity. I have appreciated the opportunity to undertake such an intriguing, multi-faceted research problem that has imparted upon me unique and useful knowledge to take with me wherever my career may take me. Through success and hardship alike, Dr. Nielson has provided the stability, patience, and understanding that have allowed me to succeed during this challenging, yet rewarding, research experience. It was a privilege to have Dr. Scott Schiff and Dr. Hsein Juang on my committee. I am honored to have two such highly respected professors who had such a substantial impact on my undergraduate education willing to assist me during this graduate research project. Their thoughts, comments, and guidance have helped shape this research as well as my understanding of the civil engineering discipline. I was duly impressed by the help provided by the OpenSees User Support team. I would especially like to thank Dr. Frank McKenna for providing outstanding technical support and expertise regarding some issues related to the OpenSees code. Alisa Neeman gave me valuable guidance regarding VEES, the visualization program she developed for OpenSees. Without the support of these developers, as well as the many other online OpenSees users who offered me their suggestions, the value of the research presented in this study would be diminished considerably. iv

6 The experience of completing this thesis has given me a new perspective of friendship. I am truly blessed to have the support of so many friends, which made the completion of this work possible. I want to express sincere thanks to all in the graduate student office who on a daily basis shared in both my frustrations and joys throughout this experience. I am especially grateful for the undying support of fellow graduate students Hossein Hayati and Jesse Chen who were unselfishly willing to offer their guidance and encouragement at times when I needed it most. It is great to know that there are friends in this world who are happy to offer their help in times of difficulty without any promise of repayment or immediate benefit to themselves. None of this would have been possible without the love and support from my family. When times were the toughest, I could feel the ties with my family strengthening around me. I am comforted by the fact that this strength was so tangible at this time in my life. I want to especially recognize the sacrifices my parents have made for me, who have always given me the freedom and encouragement to attain my goals. To my parents, and the rest of my family, I extend my deepest thanks and love. v

7 TABLE OF CONTENTS Page TITLE PAGE... i ABSTRACT...ii ACKNOWLEDGEMENTS...iv LIST OF TABLES...viii LIST OF FIGURES...ix CHAPTER 1. INTRODUCTION Problem Description Objectives and Scope of Research Outline LITERATURE REVIEW Seismic Fragility of Highway Bridges Soil-Structure Interaction Liquefaction Case Studies Involving Bridge Fragility and Liquefaction Closure MODELING OF A TYPICAL MSSS CONCRETE BRIDGE WITH SOIL COLUMNS AND LIQUEFIABLE P-Y SPRINGS Project Description Modeling Procedure Analysis Procedure Closure...64 vi

8 Table of Contents (Continued) Page 4. SEISMIC RESPONSE OF A TYPICAL MSSS CONCRETE BRIDGE WITH SOIL COLUMNS AND LIQUEFIABLE P-Y SPRINGS Introduction Ground Motions Nonlinear Site Response Analysis Seismic Response of the Soil-Structure System Closure...9. FRAGILITY ANALYSIS OF A MSSS CONCRETE BRIDGE WITH SSI AND LIQUEFACTION EFFECTS Introduction Methodology for Creating Fragility Curves Fragility Curves Considering Liquefaction and SSI Effects of Liquefaction and SSI on Fragility Closure CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH Summary Conclusions Recommendations for Future Research REFERENCES vii

9 LIST OF TABLES Table Page 3-1 PressureDependMultiYield Parameters from OpenSees User Manual (2) Summary of Wen and Wu Ground Motion Suite Summary of Rix and Fernandez Ground Motion Suite Qualitative Damage States as defined in FEMA HAZUS-MH (23) Limit States for Selected Bridge Components from Nielson (2) Component Fragilities for Wen Ground Motion Suite (12 Ground Motions) with pyliq1 Elements Component Fragilities for Rix Ground Motion Suite (96 Ground Motions) with pyliq1 elements Component Fragilities for Wen Ground Motion Suite with PySimple1 Elements Component Fragilities for Rix Ground Motion Suite with PySimple1 Elements Comparison of System Fragilities viii

10 LIST OF FIGURES Figure Page 1-1 Specific Objectives for this Study Grouped by Knowledge Area Peak Ground Acceleration with 2% Probability of Exceedance (USGS 27) Probabilistic Seismic Demand Model (Mackie and Stojadinovic 21) Permanent 2D Ground Deformation for the Humboldt Bridge After Seismic Loading (Conte et al. 22) Permanent 3D Ground Deformation for the Humboldt Bridge After Seismic Loading (Yan et al. 24) Schematic for P-y Model (Duenas-Osorio and DesRoches 26) Bridge-Pile Model for Typical SC Concrete Slab Bridge (Duenas- Osorio and DesRoches 26) Modeling of Soil-Structure Interaction for a Typical Caltrans Bridge (Shin et al. 27) MSSS Concrete Bridge Configuration (Nielson 2) Column Cross-Section Detail (Nielson 2) Elastomeric Bearing Pad Detail (Nielson 2) Pile Cap Configuration (Nielson 2) Pile-Bent Girder Seat Abutment Type Typical South Carolina Soil Profile...43 ix

11 List of Figures (Continued) Figure Page 3-7 Longitudinal Mode Shapes of 3D MSSS Concrete Bridge Model Mode Shapes of 2D MSSS Concrete Bridge Model Sample Soil Mesh Configurations Combined Bridge-Soil Model P-y Spring Configuration Typical P-y Curve With OpenSees Parameters P-multiplier Design Line (Mokwa 1999) Typical pyliq1 Hysteretic Behavior with Stiffness Degradation Abutment PySimple1 Behavior Modeling Structural Self Weight Loading Diagram Generated Response Spectra for Ground Motion Suites (a) Wen and Wu (b) Rix and Fernandez Typical Wen and Wu Bedrock Ground Motions Typical Rix and Fernandez Surface Ground Motions Acceleration Traces Measured at Top of Abutment Soil Column as a Result of Ground Motion No. 3 from Wen and Wu Ground Motion Suite Acceleration Traces Measured at Top of Abutment Soil Column as a Result of Ground Motion No. 33 from Rix and Fernandez Ground Motion Suite...74 x

12 List of Figures (Continued) Figure Page 4-6 Site PGA Measured Accelerations for Wen and Wu Ground Motions Site PGA Measured Accelerations for Rix and Fernandez Ground Motions Site PGA Amplification Ratios for the Two Ground Motion Suites Deformation and Pore Pressure Buildup Observed in Interior Soil Column for Wen Ground Motion No Deformation and Pore Pressure Buildup Observed in Abutment Soil Column for Wen Ground Motion No Deformation and Pore Pressure Buildup Observed in Interior Soil Column for Rix Ground Motion No Deformation and Pore Pressure Buildup Observed in Abutment Soil Column for Rix Ground Motion No Nonlinear Site Response Effect, Wen and Wu Ground Motion Suite Nonlinear Site Response Effect, Rix and Fernandez Ground Motion Suite Comparison Between Abutment Model Response (a) ENT-pySimple1 Model (b) Equivalent Soil Springs from Nielson (2) Seismic Response of Left Abutment Pile Elements (a) pysimple1.8m Below Ground Surface (b) pyliq1 12.7m Below Ground Surface...89 xi

13 List of Figures (Continued) Figure Page 4-17 Seismic Response of Left Interior Pile Elements (a) pyliq1 at Ground Surface (Pile Cap) (b) pyliq1 12.7m Below Ground Surface Observed Soil-Pile Seismic Response in Left Interior Soil Column for Wen Ground Motion No Observed Soil-Pile Seismic Response in Left Abutment Soil Column for Wen Ground Motion No Observed Soil-Pile Seismic Response in Left Interior Soil Column for Rix Ground Motion No Observed Soil-Pile Seismic Response in Left Abutment Soil Column for Rix Ground Motion No Probabilistic Seismic Demand Model in Transformed Log Space (Nielson 2) Example Component Fragility Curve (Nielson 2) Joint Probability Density Function for Two Continuous Random Variables Integrated Over All Failure Domains (Nielson 2) Median PGAs for Selected Components Considering Two Ground Motion Suites (a) Expansion Bearing (b) Fixed Bearing Effect of Ground Motions and Foundation Stiffness Degradation on Median PGA Fragility Values for Column Curvature Ductility Effect of Ground Motions on System Fragility Curves for MSSS Concrete Girder Bridge in Charleston, SC Considering Soil- Structure Interaction (pyliq1 Elements) xii

14 List of Figures (Continued) Figure Page -7 Comparison of System Fragility Curves Between PySimple1 and PyLiq1Models for Wen and Wu Ground Motions Comparison of System Fragility Curves Between PySimple1 and PyLiq1Models for Rix and Fernandez Ground Motions PSDM for Expansion Bearings in Bridge Model with pyliq1 Springs Subjected to Rix Ground Motion Suite PSDM for Expansion Bearings in Bridge Model with pysimple1 Springs Subjected to Rix Ground Motion Suite Observed Soil-Pile Seismic Response in Left Interior Soil Column for Scaled Rix Ground Motion No. 39s in pyliq1 Bridge Model Observed Soil-Pile Seismic Response in Left Interior Soil Column for Scaled Rix Ground Motion No. 39s in pysimple1 Bridge Model...12 xiii

15 CHAPTER ONE INTRODUCTION 1.1 Problem Description The assessment of the seismic vulnerability of transportation networks remains an important goal in the attempt to mitigate risk associated with earthquake hazards. Because highway bridges typically represent the most vulnerable components of these transportation networks, focus has been placed on the detailed assessment of seismic risk for these lifeline structures. Damage incurred to highway bridges by liquefaction and soil-structure interaction (SSI) has been well documented for the 1989 Loma Prieta and the 199 Kobe earthquakes. Earthquakes such as these have demonstrated the uncertainty associated with such ground deformation failures and unpredictable effects of interaction between bridge foundations and the surrounding soil. The use of versatile probabilistic functions called fragility curves have been recently employed to evaluate potential seismic risk for highway bridges and other systems. These fragility curves represent the probability of exceeding predefined performance levels of damage given an earthquake of a particular intensity. Fragility curves have been used for a variety of functions including seismic risk assessment, design verification, retrofit prioritization, and even post-earthquake response plans. The inclusion of fragility curves in the seismic risk assessment framework allows decision-makers to be able to make risk-based decisions with simple tools derived from reliable probabilistic methods. Though these 1

16 fragility curves have proven to be useful tools in the assessment of seismic risk, few studies have been able to directly associate the effect of liquefaction and SSI on the vulnerability of structures. The detailed relationships between ground motion, soil, foundation, and structure are difficult to predict and model. Usually the failure of foundation soils has been neglected and SSI effects have been excessively simplified in the creation of these probabilistic tools. The region of focus for this study is the Central and Southeastern United States (CSUS) which is a region of moderate seismic risk. Emphasis has been placed on this region because bridges in this region have typically been designed disregarding the possibilities of large earthquakes with historical precedence. Specifically, a typical bridge in Charleston, SC, is selected for investigation in this study because historical evidence from a previous large earthquake points to high liquefaction potential in this region. An analytical nonlinear soilstructure model considering liquefaction and SSI effects is developed and is be subjected to a large number of nonlinear time history earthquake simulations in an effort to generate fragility curves for the bridge considering these effects. 1.2 Objectives and Scope of Research The purpose of this study is to generate analytical fragility curves for a typical multi-span concrete girder bridge located in Charleston, SC considering liquefaction and SSI effects. The potential for strong ground shaking hazards coupled with soils that show susceptibility for liquefaction makes the vulnerability of highway bridges in Charleston of particular 2

17 concern. Fragility curves considering liquefaction effects are desired for bridges in this region to aid in assessing the risk associated with seismic events which have the potential to initiate widespread ground failures. These useful probabilistic tools are used by decisionmakers to help make important and potentially costly seismic risk-related decisions. This study aims to adapt a detailed methodology such that it can be used to better understand the effects of liquefaction and SSI on bridge fragility and seismic risk assessments. The following objectives fall within the scope of this research: From existing literature, decide upon the methodology best equipped to model liquefaction and SSI for a large number of ground motions. Select appropriate ground motions for use in this study. Provide documentation for the modeling of the combined soil-structure system including any modifications of the existing 3D bridge model. Conduct a seismic response analysis so that an analysis of soil-related site effects as a result of the application of selected ground motions can be conducted Evaluate any significant modifications made to the original 3D bridge model through the application of selected ground motions. Define the soil material and SSI elements used in the analytical model. Investigate the onset of liquefaction in the soil and SSI components of the model. 3

18 Generate probabilistic seismic demand models (PSDMs) for selected bridge components. Present component and system fragility curves for analysis of liquefaction effects and other observed trends. Evaluate the feasibility of creating a combined soil-structure analytical model for use in the generation of fragility curves considering liquefaction and SSI. The research scope and objectives for this study can best be presented using a flow chart highlighting specific objectives and grouping these objectives into knowledge areas as shown in Figure 1-1. The relationship between soil, SSI, and structure requires the use of a detailed combined soil-structure analytical model to include the effects of SSI and liquefaction in the fragility analysis. In hopes to take into account previously neglected significant seismic hazards associated with soil behavior, the major goal of this study is to make conclusions to aid future researchers with the development of fragility curves considering ground deformations as well as ground shaking. 4

19 Structure Convert 3D Bridge Model to 2D Model Add Pile Foundation Select Appropriate Ground Motions SSI p-y Springs Liquefiable p-y Springs Abutment Springs Fragility Create PSDMs Create Fragility Curves Analyze Results Determine Effect of Liquefaction MAKE CONCLUSIONS FOR FUTURE RESEARCH (Ground Deformation. & Shaking) Soil 2D Mesh Generator Soil Element Configuration Soil Materials Analyze Site Effects Liquefaction Figure 1-1: Specific Objectives for this Study Grouped by Knowledge Area 1.3 Outline The organization of this thesis is presented below: Chapter 2 is a literature review that defines and introduces fragility curves, soil-structure interaction, and liquefaction. Few researchers have attempted to include all three aspects in one study concerning highway bridges, but case studies of these few attempts are presented in this Chapter.

20 Chapter 3 provides a detailed project description and outlines the modeling of a combined soil-structure system utilizing soil columns in conjunction with liquefiable p-y springs. Detailed descriptions of modeling considerations and analysis steps necessary for the successful implementation of the soil, SSI, and structural elements are presented. Chapter 4 describes the basic seismic response of the soil-structure system presented in Chapter 3. Ground motions used in this study are introduced. Results and conclusions are presented for a nonlinear site analysis of the soil configuration. In addition, the seismic response of selected structural and SSI elements are verified through the application of typical ground motions. Chapter provides a detailed background of fragility curves and applies this methodology to generate component and system fragility curves for the bridge-soil model. Results are evaluated to determine the perceived effect of liquefaction and soil-structure interaction. Additional seismic response analyses are conducted to further explore these effects. Chapter 6 summarizes the previous chapters and explores the feasibility of the method presented in this study. Results and conclusions are expounded upon by offering potential research needs for future studies involving fragility curves, liquefaction, and soil-structure interaction. 6

21 CHAPTER TWO LITERATURE REVIEW 2.1 Seismic Fragility of Highway Bridges Introduction to Bridge Fragility Fragility curves serve as versatile probabilistic tools used to evaluate potential seismic risk for structural systems. Focus has been placed on the vulnerability of transportation networks in earthquake-prone regions and has required the creation of dependable fragility curves to evaluate the risk associated with highway bridges for a given seismic event. Seismic fragility curves represent the probability of exceeding predefined performance damage states as a result of various levels of ground motion intensity. Fragility can be represented by the conditional probability statement + Fragility = P( DS IM ) (2.1) where DS + represents the condition that some damage state of the structure has been met or exceeded as related to some predefined limit state and IM signifies an intensity measure of a given ground motion. This conditional probability statement can be represented in terms of previously defined limit states as ( + + ) ( + ) Fragility = P DS LS P LS IM (2.2) where LS + is the condition that a particular limit state has been exceeded. Past earthquakes have proven that bridges are typically one of the most vulnerable components of transportation systems (Hwang et al. 2). Because the performance of 7

22 entire transportation networks is closely tied to the performance of highway bridges, dependable fragility curves for these bridges are required to be able to assess the effects of earthquakes in a probabilistic framework. The benefits of creating fragility curves for highway bridges can easily be seen in their versatile implementation for a wide range of probabilistic risk-based assessment functions. Typical uses for these fragility curves include pre-earthquake planning, retrofit prioritization, and loss estimation (Choi et al. 24). Recently, fragility curves have been used as a tool for post-design verification (Nielson and Bowers 27) and for post-earthquake prioritization schemes (Ranf et al. 27). One of the most intriguing benefits of having fragility curves on file is their use in both pre-earthquake and post-earthquake applications. As the probabilistic evaluation of seismic risk becomes integrated into the design practice, the creation of fragility curves will become even more important for risk-based decisions Methodologies Used to Create Fragility Curves A wide range of methodologies for the development of fragility curves have been proposed. Included in these approaches are the fragility curves created from expert opinion, empirical data from past earthquakes, and results from analytical models. Fragility curves have been created based on expert opinion and provide an easy means to incorporate all factors which may affect the damage introduced to a given bridge (ATC 198). These expert-based curves, however, are highly subjective and depend on individual experience of the experts making decisions. 8

23 Empirical fragility curves based on post-earthquake surveys offer realistic results because they are based on actual structures subject to real ground motions. On the other hand, the relevant database is limited because data collected is specific to particular structures, soil conditions, and ground motions, and can not be derived for general purposes. The difficulty associated with finding enough bridges in a specific class that lie in a particular damage state limits the effectiveness of empirical curves. Classifying the bridges into specific damage states requires a significant degree of subjective opinion by bridge inspectors. These classifications remain highly variable and make empirical curves more difficult to create (Basoz and Kiremidjian 1997). Analytical fragility curves developed from seismic response analysis provide a means to create repeatable, general purpose representations of seismic vulnerability. The analytical fragility curves are versatile, as they can be created for a region of interest with similar bridge structures. In areas where large post-earthquake databases have not been created, analytical fragility curves must be used to quantify risk (Choi et al. 24). The Central and Southeastern United States (CSUS) is such a region with limited earthquake damage data, but where earthquakes are still a very real threat. Analytical fragility curves have also been created for new classes of highway overpass bridges constructed in California for which seismic performance data was limited and where general purpose curves were desired (Mackie and Stojadinovic 21). 9

24 2.1.3 Seismic Hazard in Charleston, SC Since the purpose of this research is to study the seismic performance of a typical bridge in Charleston, SC, some background information about the general seismic hazard in this region is presented. Like much of the CSUS, South Carolina is a region where limited earthquake data exists. The region does not lie on a plate boundary like the West Coast of the United States (WCUS), so it is assumed that movements within a plate, called intraplate movements, are the major source of earthquakes in CSUS. Even though earthquakes in the CSUS are not as frequent, these intraplate earthquakes do have the potential to produce widespread damage. Historical earthquakes such as the 1886 Charleston earthquake (moment magnitude 7.3) with estimated property damage of $-$6 million (1886 dollars) and loss of life of 6 persons (USGS 27) have revealed the threat of large damaging intraplate earthquakes in the region. Shown in Figure 2-1 is the peak ground acceleration map of the CSUS with 2 percent probability of exceedance in years provided by the United States Geological Survey (27). It can be seen in this Figure that the Charleston, SC region is recognized with moderate to high seismic risk with peak ground acceleration between. to 1.2 g. Researchers have determined that typical soil deposits in the Charleston region have a high potential of liquefaction in the event of an earthquake similar in magnitude to the 1886 earthquake (Hayati and Andrus 28). Due to the infrequent nature of earthquakes in this region, data regarding damage from the 1886 Charleston earthquake and other earthquakes in the region are not sufficient to generate empirical fragility curves for bridges in South 1

25 Figure 2-1 : Peak Ground Acceleration with 2% Probability of Exceedance (USGS 27) Carolina. For bridges in this region, such as the MSSS concrete bridge presented in this study, analytical fragility curves must be created to help quantify the risk associated with the seismic hazard. These analytical fragility curves should take into account the high risk associated with permanent ground failures associated with liquefaction Types of Analytical Fragility Curves Analytical fragility curves have been created using elastic spectral, nonlinear static, or nonlinear time history dynamic analysis methods. (Hwang et al. 2) used an elastic spectral 11

26 method to investigate the fragility of Memphis bridges. The uncertainty associated with seismic demand is introduced by a seismic force factor with lognormal distribution applied to an elastic spectrum analysis for varying levels of peak ground accelerations. While this relatively simple method remains a useful tool for practicing engineers considering regular structures, its accuracy cannot be confirmed for complicated structures with considerable inelastic behavior resulting from strong ground motions. Nonlinear static procedures provide a compromise between the computer intensive nonlinear time history analyses and the simplified elastic spectral method. These procedures have the additional benefit over the elastic spectral method by taking into account the nonlinear behavior of the structure under a static load. Shinozuka and Feng et al. (2a) used the Capacity Spectrum Method (CSM) for fragility analysis of bridges in Memphis. This method uses a pushover curve in conjunction with a reduced response spectrum. By comparing results with nonlinear dynamic procedures, the authors established that the agreement between fragility curves created with the nonlinear static method and the nonlinear time history methods decreases as nonlinear effects become more prominent. Nonlinear dynamic time-history analysis procedures are the most reliable analytical methods used to create fragility curves (Shinozuka et al. 2a). In this method, the seismic response of a structure is simulated by applying various ground motions in the form of nonlinear time histories. Because actual dynamic loadings are considered, nonlinear behavior can be captured more accurately with fewer simplifying assumptions. For typical highway bridges, the nonlinear response of the superstructure components is of particular interest. As more 12

27 complicated behavior is considered in the model, nonlinear time history analysis becomes necessary Fragility Curves Created with Nonlinear Time History Dynamic Analysis The dynamic methods generally require a detailed numerical model capable of representing the structure during nonlinear time history analyses for a wide range of ground motions. Major vulnerable components of the bridge must also be identified and limit states must be generated for each component. The seismic response of each component is assessed by quantities called engineering demand parameters (EDP). An EDP is a seismic response of a particular component of interest that is capable of indicating structural damage. A suite of expected ground motions indicative of the seismic hazard in region is applied to analytical models to represent possible expected earthquake events. Peak bridge responses, in the form of multiple EDPs, can be plotted against some given ground motion parameter associated with the particular earthquake that caused the response. The relationship between response and ground motion is called a probabilistic seismic demand model (PSDM). As shown in Figure 2-2, the PSDM represents the demand imposed on the component at a particular intensity measure as defined by the regression of the individual seismic response of the EDP. This demand model can be directly compared to predefined limit states which directly associate the probability of damage to certain levels of structure response in terms of the EDP. Fragility curves which characterize the probability of exceeding a particular damage state can be created based on this comparison between demand and capacity. 13

28 Figure 2-2: Probabilistic Seismic Demand Model (Mackie and Stojadinovic 21) After the component fragility curves have been created, the entire bridge system fragility curves can be generated by combining the component fragility curves. Nielson and DesRoches (27) have recently developed a methodology to combine component demand models into a joint probabilistic seismic demand model (JPSDM). Limit state models for the entire bridge structure have been developed by Choi and DesRoches et al. (24) based on qualitative damage states of slight, moderate, extensive, and complete (FEMA 23). Many researchers have developed fragility curves using nonlinear time history analyses for highway bridges in the CSUS region (Hwang et al. 21; Nielson 2; Shinozuka et al. 2b). Though these studies considered in detail the many components of bridge systems, the interaction between the soil and the structure was either neglected or simplified using equivalent soil springs at the base of the structure. As recent research suggests, these soil assumptions may have a considerable effect on bridge fragility (Duenas-Osorio and 14

29 DesRoches 26). Some of these concerns are addressed in the next portion of this literature review. 2.2 Soil-Structure Interaction Soil-Structure Interaction Effects One of the most difficult aspects of analytical modeling is the interaction between the soil, foundation, and structure during a seismic event. Structures are founded on highly variable soils deposits resulting in complicated relationships acting between the soil and the structure. By considering soil-structure interaction (SSI) effects, changes in system stiffness, filtering effects of ground motions transmitted to the structure, and foundation damping effects are introduced into the model. Soil-structure interaction can be subdivided into two components: kinematic interaction and inertial interaction. Kinematic interaction occurs when the foundation system interferes with the horizontal or vertical displacement of the free-field soil system under dynamic loading. This type of interaction occurs even if the soil and foundation have no mass. Inertial interaction, on the other hand, occurs due to the fact that the mass and stiffness of the soil is now connected directly to the system being analyzed. Methods have been developed to consider the kinematic and inertial components separately to be combined later during the analysis. Gazetas and Mylonakis (1998) have discussed the complexity involved in capturing these two components into a computationally efficient model. 1

30 Though the mechanics behind SSI are complex and unpredictable, typical behavior is exhibited when soil effects are considered in conjunction with the structure model. Typically, soil-structure interaction will cause the natural period of the soil-structure system to increase. In addition, radiation damping caused by geometric dissipation of waves travelling through soil will increase damping of the entire soil-structure system. These effects tend to reduce demands on the structure. However, because additional translation and rotation effects are introduced to the structure displacement demands may increase (Kramer 1996). Soil-structure-interaction can either reduce or increase demands on the structure depending not only on the soil and structure properties, but also on the frequency content of the ground motion (Kwon and Elnashai 26a). Additional displacement demands due to soilstructure interaction are especially important for slab and multi-span simply supported bridges where bridge decks have the potential to exhibit sliding, pounding, and even deck fall off (Wang and Shih 27). Because these demands are so difficult to estimate, modeling the SSI appropriately in combined soil-structure systems is of great importance so that the structural response resulting from interaction between the ground motion, soil, and structure can be examined Modeling Soil-Structure Interaction Because the nature of the SSI problem is inherently complex, computational efficiency must be considered. Full 3D finite element models (FEM) that explicitly account for the structure and advanced soil properties in the same model are the most rigorous methods currently 16

31 available, but are still poorly equipped for fragility analysis (Kwon and Elnashai 26b). The creation of fragility curves using the nonlinear time-history analytical procedure has the disadvantage of requiring a large number of ground motions to be run on the soil-structure system. Due to time and computational constraints, detailed 3D FEM models do not provide the basis from which analytical fragility curves can be created without access to large amounts of computational power, usually in the form of parallel processing. To obtain realistic SSI effects in fragility curves, compromises must be made to optimize analysis times without sacrificing relevance. One of the main objectives of this study is to explore one such compromise Vulnerability Studies Considering SSI with Equivalent Soil Springs One of the simplest methods to account for SSI is the substructure method. The soil portion of the system is represented by equivalent soil-springs which allow translation and rotation at the base of the structure (Wolf 198). In many analytical models used to create fragility curves, the soil behavior is represented by equivalent soil springs at the base of the structure. Choi et al. (24) and Nielson (2) modeled the foundation-soil system using equivalent springs for the analysis of a large number of various bridge types in the CSUS. For added accuracy in a detailed case study involving a large interstate viaduct structure, Jeremic et al. (24) calculated equivalent soil spring properties using a detailed 3D FEM containing an elastic soil mesh. The analysis showed that SSI could have detrimental, beneficial, or even insignificant effects depending on the ground motion. Kunnath et al. (26) found that the use of equivalent soil-foundation springs increased fundamental 17

32 periods significantly for the viaduct and increased the probability of bridge closure as opposed to a fixed base condition. The use of equivalent soil springs may be desirable when large numbers of bridges must be analyzed or when complicated structures are being analyzed. However, this method does not allow for inelastic behavior of the soil and SSI interaction and may not capture additional damping introduced from the soil-foundation interaction Modeling SSI with Dynamic P-y Springs One of the most promising methods to account for soil-pile-structure interaction has been the use of nonlinear p-y springs. A compromise between the substructure method and the direct 3D FEM method, p-y springs have been previously used in a wide number of static and dynamic applications in research and in practice (Kagawa and Kraft 198; Matlock et al. 1978). In this method, a collection of springs and damping elements are connected to soil elements along the depth of the foundation which represent the soil response due to base input motions. The inherent assumption with this method is that the soil-structure interaction force acting on the pile is a direct function of the displacement at that pile (Wang et al. 1998). Dynamic p-y methods provide simpler analytical solutions than computationally expensive finite element and finite difference methods that require the use of large soil meshes. The p- y relationships can be derived such that complex interactions between the pile and the soil such as gapping between pile and soil as well as radiation damping are accounted for. These 18

33 methods are becoming widely used in both the research field and in practice. The fact that the p-y methods have been accepted by both researchers and practitioners provides support that the p-y methods offer a necessary compromise bridging accuracy and efficiency. This type of compromise is required for the analytical models used in nonlinear time-history fragility analysis. Complex nonlinear p-y relationships were developed by and validated using centrifuge model tests (Boulanger et al. 1999). The p-y element contains drag, closure, plastic and elastic spring components. Radiation damping is accounted for by using a dashpot in parallel with the elastic spring component. Curras et al. (21) extended the method by considering pile groups during soil-pile-structure interaction. For both the single pile and pile group configurations, the p-y element used in conjunction with a 1D free-field soil response was capable of producing agreement with the centrifuge model tests Vulnerability Study Considering SSI with Dynamic p-y Springs Kwon and Elnashai (26b) discovered that SSI generally reduced structural demand for a reinforced concrete bridge pier under seismic loading. Dynamic p-y springs were used to model SSI between the pile foundation and the soil. Though uncertainty was added to system with the consideration of soil properties, vulnerability curves created from the analysis indicated that the probability of failure was reduced for this particular soil-structureground motion system. However, the authors concluded that soil failure limit states should also be included to more accurately represent the fragility of the system. These conclusions 19

34 lay emphasis on the need to model the soil directly in the analytical model for purposes such as permanent deformations and other soil failures such as liquefaction. 2.3 Liquefaction Definition of Liquefaction According to Kramer (1996), The term liquefaction has historically been used in conjunction with a variety of phenomena that involve soil deformations caused by monotonic, transient, or repeated disturbance of saturated cohesionless soils under undrained conditions. The generation of excess pore pressure under undrained loading conditions is a hallmark of all liquefaction phenomena. Because sands typically densify under loading, rapid dynamic loads such as those produced by earthquakes cause increases in pore pressures in the undrained condition. Saturated soils are vulnerable to this phenomenon because the undrained condition is in effect. As excess pore pressure increases, solid particles are pushed apart and effective stress decreases. The generic term liquefaction encompasses two types of behavior contributed to this loss of effective stress due to an increase in pore pressures. These two types of behavior are referred to as flow liquefaction and cyclic mobility. Flow liquefaction is a relatively rare dramatic soil failure that occurs when the static shear stress exceeds the shear resistance of the soil. This type of soil failure produces sudden, large deformations that are driven by the static shear stresses acting on the soil. 2

35 Cyclic mobility is associated with the change in hysteretic behavior in the soil as the pore water pressure increases. In contrast to flow liquefaction, cyclic mobility deformations are driven by static and dynamic shear stresses acting on the soil. Dilation and contraction phase behavior can be considerably affected by the buildup of pore water pressures. Usually cyclic mobility is observed by an increase of soil stiffness during the dilative phase of soil loading which can induce additional loading on foundations in liquefying soils. The initiation of liquefaction has the potential to affect a given site in many ways. Lateral spreading is a particular type of cyclic mobility that creates progressive ground displacements occurring in liquefying soils that are even slightly sloped. In fact, lateral spreading has been considered the most damaging type of ground failure caused by liquefaction (Bartlett and Youd 199). Brandenberg et al. (2) confirmed the significant pile demands caused by lateral spreading of soils, especially at the boundary between nonliquefied and liquefied layers. Juirnarongrit et al. (26) have tried to account for lateral spreading using the dynamic p-y method combined with a 1D site response analysis. Foundation stiffness degradation as discussed by Arduino et al. (26) is another result of liquefaction for structures supported by pile foundations. The liquefaction of soils surrounding a pile foundation causes a reduction in resistance able to be provided by the soil, thereby reducing the stiffness of the foundation. Large vertical settlement and loss of bearing capacity are vertical consequences of the initiation of liquefaction. Any of these liquefaction effects have the capability of severely damaging highway bridge structures. 21

36 2.3.2 Liquefaction in the Probabilistic Framework According to research performed by Kiremidjian et al. (23) focusing on the San Francisco region, liquefaction of soil has the potential to be the largest contributor to direct repair costs for transportation systems. This study emphasizes the need to account for liquefaction within the probabilistic framework to account for this potentially severe hazard. As mentioned previously in Chapter 1, the proposed method of accounting for SSI and liquefaction in this study is of the form + ( ) Fragility = P DS IM Soil Profile (2.3) Inherently considered in this method is the condition that the analytical model used can accurately represent both the possible permanent ground deformations of the soil profile and any damage caused to the structure due to ground shaking during any seismic event. Because combined soil-structure models require large amounts of computational and design power and are limited in the sites they describe. Equation 2.3 can be expanded to explicitly include liquefaction + ( )* ( ) Fragility = P DS L P L IM Soil Profile (2.4) where L is the condition that liquefaction has occurred. Though the probability of liquefaction given the intensity measure and a specific soil profile (the second part of Equation 2.4) is not calculated explicitly for this study, the analytical model inherently considers this probability for any loading scenario. A desirable goal would be to fully separate the geotechnical and structural components of the fragility analysis by expanding Equation 2.4 further into + ( )* ( )* ( ) Fragility = P DS LE P LE L P L IM Soil Profile (2.) 22

37 where LE signifies the liquefaction effects imposed on the structural model. For combined soil-structure models similar to that presented in this research, the probability of liquefaction effects (e.g. permanent horizontal deformations, settlement, loss of foundation stiffness) will also be considered inherently. One reason that Equation 2. is useful is because the structure, soil-structure interaction, and soil components are handled separately in the probabilistic framework. The probability of exceeding a particular damage state given liquefaction effects would be easily handled in structural models with probabilistic liquefaction input. Significant research has been conducted to adequately determine liquefaction probability conditioned on ground motion intensity measures and the soil profile. Data collected from site exploration has been used to determine the probability that liquefaction will be triggered. Methodology using CPT tests (Juang et al. 26; Moss et al. 26) and SPT tests (Cetin et al. 24) are currently in place. Further research needs to be conducted to predict the liquefaction effects including horizontal displacement and vertical differential settlement as a result of liquefaction occurring. Youd et al. (22) and Zhang et al. (24a) attempted to estimate lateral spreading effects given liquefaction while Zhang et. al (22) attempted to approximate the settlement associated with liquefaction from CPT tests. Additional focus with emphasis on the probabilistic framework is needed for horizontal and vertical liquefaction effects so that these effects can be implemented into the fragility analysis. As research in this area refines the ability to predict liquefaction effects for a given soil-structure combination, these effects 23

38 will be able to be included as input into the probabilistic framework to determine potential damage to the structure due to liquefaction occurring. One of the biggest obstacles associated with simplifying the fragility analysis considering liquefaction effects as presented in Equations 2.4 and 2. is how to handle the damage on the structure due only to the ground shaking. When the expansion of Equation 2.3 is performed, the damage due to the ground shaking and the damage due to liquefaction have been decoupled as discussed by Bird et. al (26). A method is needed to combine the probability of structural damage from liquefaction with the probability of damage occurring due to ground shaking before accurate fragility curves can be created even if the prediction of liquefaction effects is refined by further research. Little is understood about the correlation and combination of these two hazards. The research presented herein will attempt to incorporate the fragility analysis directly with the complex liquefying soil-structure interaction. Though the inclusion of liquefaction effects is not calculated from a separate probabilistic framework in this study, the inclusion of both bridge and soil in the same model inherently considers these effects. This research aims to investigate existing analytical techniques so that the effects of liquefaction on bridge vulnerability can be more readily understood. As the relationship between liquefaction and bridge fragility becomes clearer, efforts to combine ground deformation and ground shaking should be conducted so that a simplified methodology allowing the creation of fragility curves spanning a large variety of bridge types can be considered for a given region. 24

39 2.3.3 Constitutive Liquefiable Soil Models Models for liquefying soil behavior have been developed to account for the constitutive relationships and generation of excess pore pressures to account for liquefaction of sands under cyclic loads (Prevost 198; Wang et al. 199; Yang et al. 23a). These constitutive soil models are the most accurate and general representation of soil behavior available; however; to define the constitutive models many parameters are required to define elastoplastic soil behavior and pore pressure buildup. These parameters are not consistent between different constitutive models and are difficult to define with practical geotechnical laboratory or field testing (Kramer 1996). Yang and Elgamal (23b) attempted to calibrate a constitutive soil model to a database of field and laboratory data. The authors explain the rigorous optimization techniques to obtain appropriate parameter values. Yang and Elgamal have incorporated their constitutive model into the OpenSees finite element code (McKenna and Fenves 27) and have established some typical values for various sand densities (Mazzoni et al. 2). Though this soil model provides a tool to capture liquefaction during seismic loads, the model is not able to be calibrated for specific soils without a large amount of experimental data Liquefaction Incorporated into Dynamic P-y Methods Flow liquefaction and cyclic mobility are both initiated by a buildup of pore pressure in saturated sands. Whether the pore pressure buildup is a function of only the free field soil response or a direct function of the soil-structure interaction is still unknown (Klar 24). For some cases, including nonpermeable soils, the soil-structure interaction appears to be 2

40 the dominant means of pore water pressure buildup. In other cases, the free-field pore water pressure seems to be more appropriate for the analysis of liquefaction effects on piles. According to Arduino et al. (26), the soil-pile model should account for the timedependent buildup of pore water pressures in the soil. The authors assert that the pore water pressures affect not only the free-field motion of the soil, but also the p-y behavior between the soil and pile. To account for this behavior, as well as cyclic mobility and phase transformation effects also associated with liquefaction, the authors proposed that advanced constitutive models could be coupled with nonlinear site response analyses by using soil-pile interaction elements dependent on the pore water pressure. This method is expected to provide more accurate predictions of response of pile foundations. In order to approximate the effects of liquefaction during soil-structure interaction, the p-y elements previously discussed were implemented in the OpenSees finite element code and improved such that excess pore water pressure of surrounding soil elements could be monitored for potential liquefaction behavior (Boulanger et al. 23). The soil-pile interaction is scaled according to the excess pore pressure ratio to represent strength degradation as a result of undrained dynamic loading. Like the constitutive soil models, the liquefiable p-y springs have the ability to capture realistic behavior if parameters are appropriately defined for a specific soil condition. Unfortunately the parameters used to define the p-y springs are difficult to obtain. Realistic p-y relationships are needed as well as appropriate values for gapping behavior, radiation 26

41 damping, and post-liquefaction strength components. In addition, the constitutive soil models adjacent to the p-y spring must be calibrated to appropriately generate pore pressures. Because the stiffness of the liquefiable p-y spring is a direct function of effective stress in the surrounding elements, the parameters used to define the springs and the constitutive soil model are of utmost importance. The ability to capture advanced nonlinear liquefaction comes at the cost of having a large number of parameters that are difficult to define. 2.4 Case Studies Involving Bridge Fragility and Liquefaction Memphis Bridge Network Study Early methods to account for liquefaction acknowledged the impact of liquefaction on the fragility of bridges, but applied the liquefaction effects to previously generated fragility curves. Hwang et al. (2) used an elastic spectral analysis approach to generate fragility curves and then estimated liquefaction potential of the various bridge and road sites in the Memphis area. Engineering judgment was used to associate liquefaction with increased damage of Memphis bridges at those liquefied sites. The separation of the fragility curve generation and liquefaction is not desirable because liquefaction has the potential to contribute significantly to the fragility of the bridge. Not only is the liquefaction potential important to fragility analysis, but the seismic demand placed on the bridge cannot be accurately estimated when liquefaction is excluded from the generation of the demand model. Liquefied soils change the behavior of the structure and 27

42 even redistribute loads throughout the structure. Analytical models considering both the structure and the soil provide the only means to approximate unforeseeable liquefaction effects on the structures Humboldt Bridge Project The soil-pile-structure interaction for the Humboldt Bay Middle Channel Bridge in California has been studied using analytical models with the intention of assessing the seismic fragility of the structure. This Pacific Earthquake Engineering Research (PEER) testbed site was analyzed extensively for soil layer composition, soil liquefaction potential, earthquake response, and detailed nonlinear superstructure behavior. The OpenSees finite element platform was used extensively for this project. Conte et al. (22) performed a preliminary analysis on the 33m, 9-span bridge supported by prestressed concrete piles in soils potentially vulnerable to liquefaction. The bridge, piles, and soils were represented with a two dimensional nonlinear finite element model. Only the longitudinal response of the bridge was considered in the 2D model. The soil elements were derived to consider the dependence of soil stiffness and shear strength upon effective pressure, dependence of pore pressure on shear loading, and reproduction of large cyclic-mobility shear strain accumulation mechanisms. The advanced nonlinear soil elements incorporated liquefaction effects. For the purpose of preliminary analysis, soil layers were altered to have less dense material properties, thereby encouraging liquefaction at less intense ground motions. 28

43 After applying a ground motion typical of the region to the model, the soil mesh deformed considerably due to lateral spreading caused by liquefaction of the soil. These lateral spreading effects can be seen in Figure 2-3. Liquefaction of the soil was shown to create additional demands on piers, piles, and approach slabs with severe implications. The authors asserted that the 2D representation of the piles and soil unrealistically restricted the flow of the soil around piles and that additional research was underway to consider flow around piles in 2D or 3D analysis. Figure 2-3: Permanent 2D Ground Deformation for the Humboldt Bridge After Seismic Loading (Conte et al. 22) Zhang et al. (24b) extended the 2D nonlinear finite element analysis of the Humboldt Bridge by generating fragility curves for various bridge components. In this study, the probabilistic seismic hazard, demand, and fragility were considered as well as the seismic risk assessment. The soil materials developed by Elgamal and Yang (23) were embedded in 2D quad elements and placed in a finite element mesh. The limit states considered were the flexural failure of lap-spliced piers, failure of shear keys, and unseating failure. The mean annual rate of exceedance was calculated for five engineering demand parameters which help quantify the seismic risk in terms of probability when compared to limit state values. From the reliability analysis, unseating appeared to be a less vulnerable component than flexural 29

44 failure of lap-splices or failure of shear keys as a result of liquefaction and lateral spreading. Additional demands were placed on the lap splices and shear keys due to liquefaction and lateral spreading. These results verified pervious retrofitting activities performed on the bridge and helped stakeholders understand the risk associated with liquefaction under strong ground shaking. The Humboldt bridge was also analyzed using a 3D nonlinear finite element model (Yan et al. 24). Though computationally expensive, the 3D nonlinear finite element mesh provides a more accurate representation of pore water pressures, liquefied soil flow, and structural behavior. Soil materials developed by Elgamal and Yang (23) were embedded in 3D brick elements to more accurately represent soil behavior during ground shaking. In order to accelerate liquefaction, the soil layers were approximated as having looser densities than actually present. The model was subjected to ground motions expected at the site. Abutment settlement, bridge foundation movement, and pier inclination were observed after ground motions were applied. Permanent deformations are shown in Figure 2-4. The pattern of lateral spreading and settlement was similar to the previously conducted 2D analysis on the same bridge South Carolina Concrete Slab Bridge Dueñas-Osorio and DesRoches (26) developed fragility curves for concrete multi-span simply supported slab bridge components considering both soil liquefaction and nonlinear structural behavior. The authors conducted a nonlinear time history analysis with dynamic 3

45 Figure 2-4: Permanent 3D Ground Deformation for the Humboldt Bridge After Seismic Loading (Yan et al. 24) p-y springs to simplify the modeling of the soil and reduce computational time. The OpenSees platform was used to represent geotechnical and structure components South Carolina Concrete Slab Bridge Dueñas-Osorio and DesRoches (26) developed fragility curves for concrete multi-span simply supported slab bridge components considering both soil liquefaction and nonlinear structural behavior. The authors conducted a nonlinear time history analysis with dynamic p- y springs to simplify the modeling of the soil and reduce computational time. The OpenSees platform was used to represent geotechnical and structure components. Soil elements adjacent to each pile group were represented by two soil columns (longitudinal and transverse directions) capable of accounting for strength reduction caused by excess 31

46 Figure 2-: Schematic for P-y Model (Duenas-Osorio and DesRoches 26) pore water pressures. These soil elements track pore water pressures using an additional degree of freedom. Dynamic p-y springs were used to provide nonlinear interaction between the soil and the piles of the bridge. The nonlinear behavior of the p-y elements in the nonliquefied state was developed by Boulanger et al. (1999) and modified to provide strength degradation caused by liquefaction using a scaling factor proportional to mean effective stress of the adjacent soil elements (Boulanger et al 23). The concrete slab bridge was represented by a detailed three-dimensional nonlinear model created in OpenSees using nonlinear finite elements and fiber sections (Nielson 2). The effects of bearings, abutments, impact elements, bents, columns, and deck were all considered in the model. The total displacements of the columns, deck, and abutments were obtained for a suite of ground motions for both bridge models. These engineering demand parameters (EDP) were 32

47 Figure 2-6: Bridge-Pile Model for Typical SC Concrete Slab Bridge (Duenas-Osorio and DesRoches 26) used to generate probabilistic seismic demand models and fragility curves for the columns and abutments. The authors found that the component fragility curves created for the bridge model considering liquefaction were more severe than the component fragility curves created for the concrete slab bridge type generated by Nielson (2). A general trend was observed that dispersion increased for the bridge model considering liquefaction. The authors concluded that the fragility curves were dramatically affected by a critical peak ground acceleration (PGA) that triggers liquefaction. The study also confirmed the need to identify bridge components that degraded most quickly when liquefaction occurred and that component-specific liquefaction multipliers conditioned on the damage state might become a practical tool for seismic risk assessment. 33

48 2.4.4 CalTrans Bridge Study Shin and Kramer et al. (27) investigated the effect of liquefiable soils on the seismic response of a five-span concrete box girder bridge typical for California. The general configuration of the bridge is illustrated in Figure 2-7. The bridge was modeled in 2D; therefore, only the longitudinal direction was considered. Pile groups were modeled by overlaying multiple out-of-plane piles to provide a single equivalent in-plane pile. Soil behavior was modeled using a 2D FE mesh composed of quad elements embedded with soil materials created by Elgamal and Yang (23). Nonlinear dynamic liquefiable and nonliquefiable p-y springs were used to attach the soil mesh to the bridge. These springs monitored the excess pore pressure in the surrounding elements to define their interaction with the bridge pile system. Rigid base input motions were used as input to the coupled soil-structure model to obtain probabilistic seismic demand models for various bridge components. Multiple intensity measures were recorded to determine the most efficient intensity measure for each engineering demand parameter considered. Lateral spreading effects were isolated by running simulations with and without liquefiable elements. Likewise, mass inertia effects were isolated by running liquefiable models with and without the mass of the superstructure in the model. Pile demand measures were analyzed exclusively to investigate liquefaction effects, the superstructure components were not considered for the change in demand due to liquefaction effects. 34

49 Figure 2-7: Modeling of Soil-Structure Interaction for a Typical Caltrans Bridge (Shin et al. 27) Liquefaction multipliers were calculated as the ratio of the liquefied model EDP to the nonliquefied model EDP. Similarly, liquefaction multipliers were obtained for inertial and no inertial effects for the same the liquefiable case. The liquefaction multipliers provided no benefit in reducing uncertainty for the lateral spreading and provided marginal benefit in reducing uncertainty for the mass effects. The authors of this study recognized the complexity of the liquefaction problem and concluded that the liquefaction multiplier method may still be able to be applied to other soil-structure systems. This research showed that OpenSees remains a useful tool to gain understanding into the liquefaction effects on fragility curve generation and seismic risk in general. 3

50 2. Closure Several researchers have investigated the effects of liquefaction on the fragility of bridge components. The methods used to account for liquefying soil and its interaction with the structure vary widely in complexity and practice. With the exception of one early research study, all other studies have attempted to model a combined soil-structure system. In these previous studies, computational time has limited the complexity of models due to the large number of ground motions needed for the fragility analysis. While each of these studies has attempted to provide a better understanding of liquefaction and its effects on a bridge component, all have neglected to investigate the impact of liquefaction on the entire system fragility. The use of liquefiable p-y springs appears to be the best compromise between realistic liquefaction effects and computational efficiency. Unfortunately, even in this simplified framework, the modeling of soil and soil-structure interaction elements capable of capturing liquefaction requires the use of advanced parameters that are difficult to estimate from current experience. To further complicate the analysis, the bridge response is unpredictably dependent on the soil, SSI, structure, and the ground motion. The inclusion of the soil in the model has the possibility of increasing, decreasing, or having no effect on the structural response of a structure. As seen in this literature review, liquefaction and SSI have the potential to affect bridge fragility significantly. Because fragility curves have proven their usefulness in earthquake preparation and response, accurate fragility analyses containing SSI and liquefaction are 36

51 necessary to better approximate the demands on the structure. The inclusion of liquefaction and SSI into the probabilistic framework requires researchers to investigate this difficult-tomodel phenomenon in an effort to better approximate seismic risk associated with highway bridges. 37

52 CHAPTER THREE MODELING OF A TYPICAL MSSS CONCRETE BRIDGE WITH SOIL COLUMNS AND LIQUEFIABLE P-Y SPRINGS 3.1 Project Description Target Bridge Description The bridge analyzed for the purpose of this study is a multi-span simply supported (MSSS) concrete bridge typical of the Central and Southeastern United States (CSUS). MSSS concrete bridges are the most typical bridge category catalogued in the National Bridge Inventory database for the CSUS with approximately 18.9 % of the 163,433 bridges catalogued (Nielson 2). The bridge is assumed to be located in Charleston, SC, for the purpose of defining an appropriate soil profile for the site so that liquefaction and soilstructure interaction (SSI) effects can be explored. A detailed description of the MSSS concrete bridge model is provided in the work by Nielson (2). Bridge components, including column details, were determined from existing bridge plans and pre-existing work (Choi 22). The bridge consists of three spans of 12.2, 24.4, and 12.2 m for a total length of 48.8m. The bridge configuration is shown in Figure 3-1. Each bridge bent consists of a mm wide by mm deep concrete bent beam with three 914 mm diameter, 46 mm tall concrete columns spaced m on center. Figure 3-2 shows a typical pier column obtained from Nielson (2). The columns 38

53 Figure 3-1: MSSS Concrete Bridge Configuration (Nielson 2).8 mm 12 - # 29 bars mm #13 3 mm o.c..8 mm Figure 3-2: Column Cross-Section Detail (Nielson 2) 39

54 contain 12 #29 bars for longitudinal reinforcement and #13 transverse bars spaced at 3 mm. The design strength of concrete is considered to be 2.7 MPa with yield strength of reinforcing steel considered to be 414 MPa. The precast concrete bridge girders are supported by fixed and expansion elastomeric bearing pads in conjunction with dowel rods as seen in Figure 3-3. The bearings support horizontal loads through friction in the elastomeric pads caused by the weight of concrete girders. In addition, dowel rods embedded in the concrete supports and elastomeric pads protrude into holes in the bottom of the concrete girders to provide additional horizontal resistance during an earthquake. The expansion bearings and fixed bearings are essentially the same, with the expansion bearings having a slotted hole for the dowel as opposed to a round hole. The bearing pad types alternate between fixed and expansion type along the length of the bridge. Columns are supported by individual reinforced concrete footings which also serve as pile caps. A lap splice is used at the column-footing connection. The footing dimensions are 2438 mm square with thickness of 192 mm. Reinforcement is placed at the bottom of the footing. Eight 34.8 mm square precast concrete driven piles of length 12.7m are embedded at the base of footing without positive connection. See Figure 3-4 for the pile cap configuration. The bridge abutment type is a pile-bent girder seat abutment illustrated in Figure 3-. The abutment itself is approximately 1.2m wide with two 2.8m wingwalls used to develop additional passive soil pressure during lateral loading located on either side. Ten 4

55 Figure 3-3: Elastomeric Bearing Pad Detail (Nielson 2).46 m.76 m Y X.76 m.46 m.46 m.76 m.76 m.46 m Figure 3-4: Pile Cap Configuration (Nielson 2) 41

56 Back Wall Bridge Seat Vertical Piles Figure 3-: Pile-Bent Girder Seat Abutment Type 34.8 mm square precast concrete vertically driven piles, 12.7m long, are distributed along the width of the abutment Target Soil Profile Description The soil profile used in this study consists of sandy layers typical of the coastal region of South Carolina and is illustrated in Figure 3-6. The soil profile for this study is taken to be similar to the profile presented in research by (Duenas-Osorio and DesRoches 26) which was obtained from a sample of 4 borings across 1 different bridge sites along the coast of South Carolina. The SPT average blow counts presented by the authors are used to obtain basic soil descriptions. For the soil profile beneath the abutments, an overlying 6.3m thick medium-dense unsaturated sand layer is assumed to approximate compacted fill material to create the approach slope for the bridge. 42

57 6.3m Medium-Dense SAND γ = kn/m 3 φ = m 3.81m.8m 3.81m Medium SAND γ = kn/m 3 φ = 33 Loose SAND γ = kn/m 3 φ = 29 Medium SAND γ = kn/m 3 φ = 33 Medium-Dense SAND γ = kn/m3 φ = 37 Soil Profile at Abutments Medium SAND γ = kn/m 3 φ = 33 Loose SAND γ = kn/m 3 φ = 29 Medium SAND γ = kn/m 3 φ = 33 Medium-Dense SAND γ = kn/m3 φ = 37 Soil Profile at Interior Pier Figure 3-6: Typical South Carolina Soil Profile 3.2 Modeling Procedure Justification for 2D Model The OpenSees finite element code developed by McKenna and Fenves (27) is used extensively as the platform for analysis. This open-source code provides a wide range of powerful applications necessary to create combined soil-structure analytical models. Although OpenSees provides the finite element code necessary to analyze a full 3D soil mesh interacting with a 3D structure, the long run times require the use of parallel computing for analysis of all but the simplest problems. From preliminary testing, 3D soil elements are found to require extensive computational time for a desktop machine. As parallel computing is out of the scope of this research, and computational run times are a potential controlling factor as a result of the sheer number of ground motions required to 43

58 generate fragility curves, a simplified 2D analysis is performed in this study. Furthermore, the bridge type being considered in this study has been shown to be dominated by its longitudinal behavior (Choi 22) and hence further justifies the use of 2-D longitudinal models Modeling of the MSSS Concrete Bridge in 2D The 3D MSSS Concrete bridge model created by Nielson (2) makes use of linear elastic and nonlinear elements to represent bridge behavior during gravity and seismic loadings. The bridge columns and bent cap are both modeled using detailed nonlinear fiber section elements. The bridge deck is modeled using elastic beam-column elements. Fixed and expansion elastomeric bearing pads including dowel connection behavior are represented with nonlinear zerolength springs. Equivalent springs are obtained for the abutment-pile and foundation-pile interaction with the soil. The 3D bridge model provided by Nielson is converted to a 2D model. According to Nielson (2), the bridge exhibited a dominant vibration mode in the longitudinal direction with a period of.62 seconds and mass participation of 84.%. The second and third modes are transverse and torsional modes, but the fourth mode is also longitudinal with a period of.33 seconds. Because the dominant motion appears to be in the longitudinal direction, the 2D model is created to represent only the longitudinal behavior. The 2D model sacrifices transverse bridge behavior for the benefit of faster analysis times. Inherent in the 2D 44

59 assumption, errors will be present with out-of-plane dynamic behavior of the structure, as transverse and torsional modes cannot be considered. To simplify the 2D model, out of plane (transverse) nodes that would occupy the same location in 2D are compressed to a single node. Springs and columns which would occupy the same locations in 2D space are connected by multiple elements to the single 2D node. Bent cap beams are replaced by rigid elements that represent the depth of the bent beam in 2D.. An eigenvalue analysis is performed for the 2D bridge to verify similar mode shapes and mass modal participation relative to the 3D bridge. The equivalent soil springs calculated by Nielson were attached at the base of the columns and abutments for the purpose of this verification. The first two modes showed longitudinal behavior. The first mode had a period of.62 with approximately 84% mass participation and a second mode of.33 seconds. As can be seen in Figure 3-7 and Figure 3-8, the mode shapes and periods compare favorably between the 3D and 2D models Modeling of Bridge Foundations Nonlinear pile behavior has been documented to be a significant factor for some major earthquakes, especially under lateral spreading conditions (Finn and Fujita 22); however, elastic pile elements are computationally efficient and may provide similar results for certain ground motions and soil conditions. Though the inelastic piles would most likely provide better accuracy, there are still some questions about including inelastic behavior in piles 4

60 Mode 1 T=.62 sec Mode 4 T=.33 sec Figure 3-7 : Longitudinal Mode Shapes of 3D MSSS Concrete Bridge Model Mode 1 T=.62 sec Mode2 T=.33 sec Figure 3-8 : Mode Shapes of 2D MSSS Concrete Bridge Model (Gazetas and Mylonakis 1998). In the literature, the authors contend that piles are typically designed such that they behave in the elastic range. However, even when piles are properly designed, conditions such as loose soil layers sometimes dictate the consideration of inelastic behavior. For this project, the use of inelastic pile sections would greatly increase the number of elements required as each pile would require its own fiber section. For computational efficiency, an equivalent linear elastic beam-column element is used to represent each pile 46

61 group. Each pile is assumed to be 12.7m long and is divided into ten 1.27m segments. This element spacing is consistent with the height of each soil mesh element Soil Modeling For use in current and future soil modeling purposes, a mesh generator is written as part of this study for use in OpenSees. The mesh generator allows the user to define up to five soil layers of 2D-quad elements for any size mesh. Element size in the vertical and horizontal direction can also be input by the user. One limitation of the generator is that variable width elements, generally desired for problems involving soil-pile interaction, are not currently implemented except at the boundary elements. Another limitation is that the user must define any sloped surfaces manually. Even with these limitations, the mesh generator saves the user much time from having to manually input each node coordinate and define each element individually. Accompanying the mesh generator, additional procedures are included that allow the user to integrate pile elements into the mesh by providing required dummy nodes to attach p-y springs from the soil to the pile structure. These programming features will be able to be used in additional future soil-structure interaction problems. Figure 3-8 shows some sample meshes created using this mesh generator for the typical South Carolina soil profile presented earlier in this chapter. The 2D Full mesh required writing additional procedures to remove elements and provide nodal coordinates for the abutment slopes. For saturated soil layers, the PressureDependMultiYield (PDMY) material is embedded into a FluidSolidPorous (FSP) material, thereby coupling fluid and soil behavior (Mazzoni et al. 2). The PDMY-FSP combination represents a fully undrained saturated soil (below the 47

62 2D Soil Column Mesh 2D Full Mesh Figure 3-9: Sample Soil Mesh Configurations water table), while a PDMY material by itself represents unsaturated soil (above the water table). Both unsaturated PDMY materials and combined PDMY-FSP materials are implemented in 2D-quad elements to create a 2D finite element mesh. The OpenSees Command Manual has some suggested values for typical sand descriptions to be entered into the PDMY constitutive soil model (Mazzoni et al. 2). The parameters that are used as input for the soil layers, including strength parameters and some less typical properties defining volume change and pore pressure buildup, are provided in Table 3-1. A simple description is provided for each parameter. Originally, the scope of this research was such that the 2D full mesh would be used to investigate liquefaction effects, but after preliminary testing revealed long run times and suggested the use of vertical t-z and q-z springs, which represent the friction and bearing tip resistance on the pile, the scope was simplified to include a simplified 2D soil column method (Boulanger et al. 1999; Shin 27). The quad elements consisting of PDMY-FSD 48